Chapter 5: Further Pure 1: The t-formulae

A-level Further MathsFurther Pure 1 & 24 topicsHigher

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alevel · further-maths · Further Pure 1 & 2 · All papers

Releases 1 August 2026

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Further Pure 1: The t-formulae: Edexcel Further Maths Optional Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions32 marks64 min

standard / hard / synoptic

8 marksfindstandardEdexcel

FP05-1 Find the required result for Further Pure 1: The t-formulae. Given Use t = tan(

\theta

/2) to solve 3 sin

\theta

+ 4 cos

\theta

= 2 for 0

\leq

\theta

< 2pi. Use substitute sin

\theta

= 2t/(1+

t^{2}

) and cos

\theta

= (1-

t^{2}

)/(1+

t^{2}

). (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksshow thathardEdexcel

FP05-2 Show that the equation reduces to 6t + 4(1 -

t^{2}

) = 2(1 +

t^{2}

) for Further Pure 1: The t-formulae. Start from Use t = tan(

\theta

/2) to solve 3 sin

\theta

+ 4 cos

\theta

= 2 for 0

\leq

\theta

< 2pi. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksdeterminehardEdexcel

FP05-3 Determine the requested value in this structured Further Pure 1: The t-formulae problem: find all

\theta

values in radians. Use the same data: Use t = tan(

\theta

/2) to solve 3 sin

\theta

+ 4 cos

\theta

= 2 for 0

\leq

\theta

< 2pi. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 markshencesynopticEdexcel

FP05-4 Hence use the result the equation reduces to 6t + 4(1 -

t^{2}

) = 2(1 +

t^{2}

) to complete the extension for Further Pure 1: The t-formulae: find all

\theta

values in radians. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

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4. Further Pure 1: Inequalities

6. Further Pure 1: Taylor Series

Key learning objectives

Understand the key principles behind Further Pure 1: The t-formulae.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.